JEE Main 2021 · 24 February · evening · Single correct · +4 / −1

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

  1. (a) 10⁻² nm
  2. (b) 10⁻¹ nm
  3. (c) 10⁻³ nm
  4. (d) 10⁻⁴ nm
Answer and solution

Answer (c) 10⁻³ nm

Solution

Physics sir · 4 steps

The shortest wavelength comes from one electron handing all its energy eV to a single photon.

  1. Cutoff wavelength. Each electron reaches the target with kinetic energy eV. The shortest wavelength comes from an electron that gives all of this energy to a single photon.

    λₘᵢₙ = hc/eV

  2. Handy value of hc. Take hc = 1240 eV nm. With V = 1.24 × 10⁶ V, the photon energy is 1.24 × 10⁶ eV.
  3. Put in numbers. λₘᵢₙ = (1240 eV nm)/(1.24 × 10⁶ eV) = 10⁻³ nm.
  4. So. The shortest wavelength is 10⁻³ nm, which is option (c).

The idea to keep. For any X-ray cutoff, use λₘᵢₙ = 1240/V nm with V in volts. Keep track of whether your hc value is in nm or in ångström.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 110 times in JEE Main since 2020. This question is from 2021.